The vaccinated and the unvaccinated

Some COVID statistics to ponder.

Misinformation and misunderstanding about vaccine efficacy have abounded recently, potentially sparked by what seemed to be worrying data out of Provincetown, Massachusetts, reported last week by the CDC.

The agency’s investigation revealed that 74% of the 469 COVID-19 cases in that outbreak occurred in fully vaccinated people.

But that doesn’t by any stretch of the imagination mean that three-quarters of vaccinated people are getting COVID.

In addition to this being one particular outbreak, as vaccination rates increase overall, a larger proportion of cases will occur in the vaccinated — it’s just simple math.

Katelyn Jetelina, PhD, MPH, an epidemiologist at the University of Texas Health Science Center at Houston, explained the concept of base rate bias back in June after the Israeli health minister said that about half of infections were occurring in vaccinated people.

“The more vaccinated a population, the more we’ll hear of the vaccinated getting infected,” Jetelina wrote, noting that 85% of Israeli adults were vaccinated at the time.

If there were four COVID cases out of 100 people, for example, with two occurring in vaccinated people and two occurring in unvaccinated people, that would be 50% of cases occurring in vaccinated people.




But the more important number to look at would be infection rates among the separate groups — which would be a 13% infection rate in the unvaccinated, and a much smaller infection rate of 2% in the vaccinated.

That would strongly indicate that vaccines are working.

Massachusetts’s most recent data on breakthrough cases indeed indicate that vaccines are working remarkably well in that state. As of July 31, there were 7,737 breakthrough infections among 4.3 million fully vaccinated people. Of these, 395 required hospitalization, and 100 died.

With that large of a denominator, the percentages are reassuring: 0.18% of fully vaccinated people had a breakthrough infection; 0.009% went to the hospital; and 0.002% died.

Source: The vaccinated and the unvaccinated

It might be worth reviewing Bayes’ Theorem.